In Black Panther: Wakanda Forever there is a reference to the Collatz conjecture. When Shuri is on Riri Williams’ campus as she knocks on her door, she looks past this sign:

Solve or DONT KNOCK Collatz Conjecture 3(x)+1 

The Collatz conjecture is a famous open conjecture in math, which means it is unanswered. It is also famous for coming from an extremely simple premise. This sign is meant to be humorous because the conjecture has been open for over $80$ years and is widely considered to be an unproductive use of time.

The Conjecture¶

The Collatz conjecture is as follows:

1. Pick a positive integer, $x$.
2. If the integer is even, then half it. Otherwise if it is odd, multiply it by $3$ and add $1$.
3. Repeat step $2$ indefinitely The conjecture states that for all positive integers $x$ that following this algorithm will eventually reach the loop of $(4, 2, 1)$. The $(4, 2, 1)$ loop is where all tested integers will end up. $4$ is even so it becomes $2$, $2$ is even so it becomes $1$, and $1$ is odd so it becomes $3(1)+1$ is $4$.

Current Status¶

Currently the only known loop of numbers is $(4, 2, 1)$, and finding another loop would disprove the conjecture and lay rest to this problem. It is currently estimated that if a loop exists then it is likely to contain at least $137{,}500{,}000{,}000$ numbers, with no number smaller than $3 \cdot 2^{69}$.

It is the opinion of the writer that the Collatz conjecture is solvable, but we have not yet discovered the mathematics needed to do so.

Sources¶

• https://cs.uwaterloo.ca/journals/JIS/VOL26/Hercher/hercher5.pdf